Processes are defined with (a) n = 3 and k = 1, (b) n = 3 and k = 2, and (c) n = 4 and k = 1. Colored transitions in the observed schematic time series are correspondingly colored as state transitions in the Markov Process below the time series, and also designated in the state transition matrices. Note that the time series are identical between (a), (b), and (c). For clarity, each line between states in the central state-transition graph of (b) is condensed to represent both a forward and a reverse state transition.